Pat the cheeks dry with paper towels; season generously with salt and pepper.

Warm the olive oil in a large sauté pan over medium-high heat. When it is very hot but not smoking, add the pork cheeks in a single layer, without crowding. Sear until nicely caramelized, 5 to 10 minutes on each side. (Make sure to listen for a nice sizzling sound.) Transfer the cheeks to a deep baking dish, reserving the fat in the pan.

Return the pan to medium heat and add the onion, shallots, and garlic. Sauté until brown; season with salt and pepper. Add the bay leaves, thyme, and sherry; deglaze the pan. Scoop the mixture over the pork, and add enough stock to cover the meat; season again with salt and pepper. Cover with aluminum foil and bake for 3 to 3 ½ hours, or until the meat is very tender.

Divide the pork cheeks among four warm plates and top with a spoonful of the romesco sauce; pass the remaining romesco on the side.

Romesco Sauce:

4 Roma tomatoes, peeled and quartered

2 red bell peppers, stemmed, quartered, and seeded

1 small onion, peeled and quartered

8 whole garlic cloves, peeled

1 tablespoon fresh thyme leaves

1 ancho chile, seeded and rehydrated in warm water

1/4 cup toasted almonds

1 slice toasted bread, crust included

About 1 tablespoon sherry vinegar

1 tablespoon smoked paprika

1/4 to 1/2 cup olive oil, for cooking and blending.

On a rimmed baking sheet, spread the tomatoes, bell peppers, onion, and garlic cloves; drizzle generously with olive oil and scatter with thyme, and a little salt and pepper. Place under a broiler set to medium heat, or in a 400° oven. Cook until lightly charred and cooked through, tossing occasionally.

In a blender, combine the vegetables, ancho chile, almonds. Bread, vinegar, and smoked paprika. Blend until smooth adding olive oil in a fine stream to emulsify the romesco, just enough to yield a slightly chunky paste. If the mixture will not move easily on the blender, add a little bit of the braising liquid from the pork cheeks. Adjust the seasoning to your taste with additional salt, pepper, smoked paprika, and/or sherry vinegar. Depending on the acidity level of the tomatoes and peppers, the romesco might need a little less or more sherry vinegar.